Pith Number

pith:W4TRQC3O

pith:2026:W4TRQC3OW4B22O2XCGPAS6K5TD

not attested not anchored not stored refs pending

On the Dax invariants of $S^2$-bundles over surfaces

Qizheng You

arxiv:2607.04695 v1 · 2026-07-06 · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4TRQC3OW4B22O2XCGPAS6K5TD}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-07T02:19:58.511547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b727180b6eb703ad3b57119e09795d98cd2aa23e575e148323eeba3217c9926b

Aliases

arxiv: 2607.04695 · arxiv_version: 2607.04695v1 · doi: 10.48550/arxiv.2607.04695 · pith_short_12: W4TRQC3OW4B2 · pith_short_16: W4TRQC3OW4B22O2X · pith_short_8: W4TRQC3O

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W4TRQC3OW4B22O2XCGPAS6K5TD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b727180b6eb703ad3b57119e09795d98cd2aa23e575e148323eeba3217c9926b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f084c3a213227212432df87d7876c114f09a45af31da2a1f56e5f1d3cc0df781",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-07-06T05:54:58Z",
    "title_canon_sha256": "5e51a096f9cc74e3767693062bc7c31e293f49f1e69b972fa5ba2d07eac45055"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04695",
    "kind": "arxiv",
    "version": 1
  }
}